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Luhn algorithm. The Luhn algorithm or Luhn formula, also known as the " modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers. It is described in US patent 2950048A, granted on 23 August 1960. [ 1]
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = be mod m. From the definition of division, it follows that 0 ≤ c < m . For example, given b = 5, e = 3 and m = 13, dividing 53 = 125 by 13 leaves a remainder of c = 8 .
Modular multiplicative inverse. In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m. [ 1] In the standard notation of modular arithmetic this congruence is written as.
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
Frequency synthesizer. A frequency synthesizer is an electronic circuit that generates a range of frequencies from a single reference frequency. Frequency synthesizers are used in devices such as radio receivers, televisions, mobile telephones, radiotelephones, walkie-talkies, CB radios, cable television converter boxes, satellite receivers ...
A modulus is a formal product [3] [4] where p runs over all places of K, finite or infinite, the exponents ν ( p) are zero except for finitely many p. If K is a number field, ν ( p ) = 0 or 1 for real places and ν ( p ) = 0 for complex places. If K is a function field, ν ( p ) = 0 for all infinite places. In the function field case, a ...
One problem of CVD processes is the high variability in the nanotube's characteristics [86] The HiPCO process advances in catalysis and continuous growth are making CNTs more commercially viable. [87] The HiPCO process helps in producing high purity single-walled carbon nanotubes in higher quantity.
Barrett reduction. In modular arithmetic, Barrett reduction is a reduction algorithm introduced in 1986 by P.D. Barrett. [ 1] A naive way of computing. would be to use a fast division algorithm. Barrett reduction is an algorithm designed to optimize this operation assuming is constant, and , replacing divisions by multiplications.